texts: Should I fit a function to this lightcurve?

texts:
I am creating a light curve for the duration of a binary system in order to find out the duration of the eclipse. I am unsure as to whether to fit a function to the data (is it appropriate) as by fitting the function I am expressing that I think that the data lies within this region.
I was thinking of maybe doing the fit piecewise but I am unsure if I should even fit it at all. Any reading material or help would be great. I just need a pointer in the right direction.
I've attached two images. One plot without a fit and one plot with a cubic function fitted to the graph.
Many thanks in advance,
Owen.


texts: The giant impact hypothesis is a theory to explain how the moon was formed. What evidence is there that supports the theory and led us to find the current theory?


texts: How far could be an object from the Sun and still be under the influence of its gravitational field?

texts: I'm trying to see how far can our star reaches with its gravity. I'm asking if anyone could give info as to what's our star's limit or the furthest object found in our solar system.


texts: Will the Sun rotate slower in red giant form?

texts: When the Sun runs out of hydrogen to fuse it will grow bigger in size and my question is does it rotate more slowly, like a spinning ice skater extending their arms to reduce angular velocity? What consequences will accompany with a slower dynamo (big ball of plasmas), such as more frequent solar flares or perhaps more dark spots?


texts: How would the combined masses of the Centaurs or the scattered disk compare to the combined mass of the asteroid belt?

texts:
I'm interested in finding the combined mass of the Centaurs and the scattered disk. I looked around but I wasn't able to find any estimates. This seems to suggest that either the combined masses of the Centaurs or the scattered disk are negligible in comparison to that of the asteroid belt, or nobody ever thought of making an estimate. All I could find was that the asteroid belt is approximately 0.04 moon masses and that the Jupiter Trojans are approximately 1/5 of the mass of the asteroid belt. My feeling is that these combined masses should be way more than that of the Jupiter Trojans.

Thank you in advance, and yes, I tried Wiki.


texts: calculation of characteristic expansion time of the universe

texts:
Hubble's constant is estimated at 15km/s at a distance of million light years, without considering effects of mutual gravity, relativity, etc.
I am trying to calculate the characteristic expansion time of the universe.
Its formula is given as reciprocal of the Hubble constant, because time is distance by velocity. But:

$$v=kx$$

This implies that velocity and distance are exponential functions of time and so time cannot simply be calculated by dividing 1 million light years by 15km/s.
So what am I missing? Why is the characteristic expansion time simply the reciprocal of Hubble's constant?


texts: Why was the July 27th 2018 lunar eclipse not visible in North America?

texts:
I was just wondering if it had anything to do with the fact that last year we were blessed with the opportunity to see the total solar eclipse in our neck of the woods. So this is the universe's way of making things 'even'. Or is it pure chance and luck?

Jokes aside, there is probably a physics explanation regarding tidal forces or angular momentum, so I am curious how these factors affect which parts of the world get to witness the event.


texts:
I have a simple question :
How to prove the following relation :

The comoving distance to an object at redshift $z$ can be computed as

$$r(z)=\dfrac{c}{H_{0}} \int_{0}^{z} \dfrac{\mathrm{d} z}{E(z)}$$
from the relation :
$$r(t)=\int_{0}^{t} \dfrac{c\mathrm{d} t}{R(t)}$$
I tried to use with the definition : $1+z= \dfrac{R_{0}}{R(t)}$ but I can't conclude.
Any help is welcome.
UPDATE 1 : @Tosic's demonstration seems to be correct. But the factor $R_{0}$ is not disappearing. Indeed, If I do :
$$\dfrac{\text{d}(1+z)}{\text{d}t} = \dfrac{\text{d}z}{\text{d}t} = -\dfrac{H(t)}{R(t)}\,R_{0}$$
which implies :
$$\int_{0}^{z} \dfrac{c\text{d}z}{H(z)} = \int_{0}^{t}c\text{d}t\dfrac{R_{0}}{R(t)} = R_{0} \int_{0}^{t}\dfrac{c\text{d}t}{R(t)}$$
How to get rid of the factor $R_{0}$ ? Since if I multiply the comoving coordinate $r(t)$ by $R_{0}$, I get the cosmological horizon (the limit of observable universe if I integrate up to $z=1100$), don't I ?


texts: Do moons experience periods of no sunlight when orbiting "behind" their planet?

texts:
I'm writing a story that takes place on the Saturn moon Iapetusand I was thinking that especially since Iapetus only has an inclination of about 17 degrees from the ecliptic, wouldn't there be a point during its orbital period where it orbits "behind" Saturn — that is to say, Saturn is directly between Iapetus and the Sun — and doesn't get any direct sunlight?
Is that correct or am I missing a detail here?
If it is true that moons like Iapetus experience these periods of no sunlight, how difficult would it be to calculate roughly how long this period would be using the inclination and the orbital period?


texts: When a planet or a satellite turns around itself, its called a rotation. When a planet goes once around the Sun, it's called a revolution. What do you call it when a satellite goes once around its planet? Is it also a revolution? But then how do you disambiguate with the satellite having gone once around the Sun?


texts: Contradiction between Theory of Relativity and Newton's Law of Universal Gravitation?

texts: Newton's Law of Universal Gravity states that an object will accelerate constantly as it falls. Let's assume an object falling into a black hole. According to Newton's Law, when it reaches the event horizon it must be traveling at c, because c is the escape velocity at the event horizon. Therefore, after it passes the event horizon, it must continue to accelerate past c, yet theory of relativity states that it's never gonna happen. So, in this condition, what will the object do?


texts: Was the Sun's gravitational lensing observed in other solar eclipses than the one in 1919?

texts: In 1919 the gravitational lensing by the Sun has been observed during a total solar eclipse. Did someone observe the lensing in any other total eclipses? Last year there was a total eclipse in Chile and there were many scientists observing it. Did they see the stars in different places too? I mean, today it must be even easier to observe it with current telescopes or something. But there is no mention of any other observations than the one in 1919, is there?


texts: Can we know whether any distant galaxy is moving away in same direction or in opposite direction w.r.t. our galaxy?

texts:
The Hubble law states that the recessional velocity of a galaxy is proportional to its distance from us.
It takes redshift and angular sizes (for distance) of the galaxy to determine velocity, and thus rate of expantion.
But I guess the factor of direction in which the galaxy is moving may substantially affect the 'expantion rate' calculations. i.e. If the galaxy A is moving in same direction as ours, will have less relative speed and the galaxy B moving in opposite direction will have more relative speed. The actual local speed may be the same.
I wonder whether this fact can be considered when we determine the expansion rate?


texts:
From the wiki article about eccentric anomaly follows:

$$\cos E = \frac{x}{a}$$
$$\sin E = \frac{y}{b}$$

where E - eccentric anomaly, a - semi-major axis, b - semi-minor axis, P = P(x,y) a point on elleptic orbit. So if you know an E, you can find a position on an orbit:

$$x = a \cos E$$
$$y = b \sin E$$

However, from article on Kepler's eqution follows:

$$x = a (\cos E - e)$$
$$y = b \sin E$$

Please, help to understand why these formaluae differ? I expect them to be the same.


texts: Did I see the dragon capsule on Friday night?

texts:
I live just south of Sydney Australia, and I went outside to watch the ISS pass overhead on Friday night. The ISS was following a smaller object easily visible to the naked eye.

Sydney time 20.43 or UTC 9.43. (Friday March 8) The smaller object was ahead of the ISS by maybe 25 degrees. Appeared to be moving at exactly the same speed and trajectory.

Was this the the SpaceX Crew Dragon capsule? Sorry if this is the wrong place to ask.


texts:
In the last few days I experienced two events I cannot explain. I watch the sky since I was a child so I'm aware of most events like satellites, ISS, Iridium flares, etc...
First event
It was about 22:30 local time and I was located in the central Italy. I was looking in the nearby of Hercules and Corona Borealis when some degrees at left of Arturo (say near M5) a white light flashed shortly. The flash was very short, I think below 150 ms without any fade. Because it was so short I cannot say if it was moving or not, but the other strange thing is it's apparent diameter. It was larger than any other star or planet and without any difference of luminosity between the center and the border. I mean, it was like a small disk with a matte surface and a uniform white light. I can estimate it's magnitude about -2 (slightly less Jupiter in these days). It was not like an Iridium flare at all.
Second event
Yesteday, norther Italy, 1:30 AM local time. I saw what looked like a very bright satellite in SW/NE orbit. But there were few strange things:

as far as I know, it was too late for any satellite to be illuminated by the sun for such a bright magnitude. It was as bright as Venus at its maximum brightness (I would say at least -3.5).

it was composed of two distinct lights, very close together. At first I thought it was a plane from the nearby airport with landing lights still on after takeoff, but I know them and this was different. Furthermore there were no red/green lights nor strobo. And the lights were too close for a a plane below 10000 feet. Then they didn't change their brightness across the sky, like landing lights do.

it moved across the sky like the ISS does, and just few degrees from my zenith it disappeared instantly without any fading.

Any idea of what they might be?


texts:
I would like to help find sources or calculations for the following dates found in Wikipedia (in French). The next Uranus transit from Neptune will happen :
1. October   38172
2. August   111551
3. November 124067

Would you please help me find sources or calculations stating these three dates?


texts: Identify moving object in the sky at night?

texts:
Last night in the Carribean, I was looking at the sky at about 8PM EST, and I noticed this really tiny object moving pretty fast from left to right, just between the two stars in the photo. It's very difficult to see and after a while it just disappears.
Somebody told me they had seen it a few days ago going the same exact direction and more or less at the same time.
Can anyone identify this moving object?
I'm including the picture of where I saw it, but you can't see the object. I didn't bother taking a picture while it was moving because it's so tiny that I had trouble finding it myself.
Also, is there a way for an amateur like myself to identify these objects?


texts: Universe as 2d sphere surface - a round trip?

texts:
If Universe's analogy is 2D surface of the sphere, could we come around in circle? Say on Earth you decided to travel straight in one direction, after completing one full circle you'd find yourself at exact spot where you started.

Now, if we up that up by 1 dimension and apply it to our Universe, would the same thing happen if we pointed the rocket in a straight line? I.e. would the rocket come back to earth?


texts: It takes 8 minutes for the sun's light to reach earth. If the sun were to instantly disappear, what would happen? I imagine that Earth would fly away on a path tangential to its orbit. What would happen to our heat and light during those first 8 minutes after the sun's disappearance?


texts: How is the Dating of Samples of Cosmic Objects Performed, Including Pre-Solar Dust?

texts:
In the new Space.com article 7 billion-year-old stardust is oldest material found on Earth I had read about some pre-solar grains dating back to 7 billion years. What techniques are used in calculating age of these grains?
Are they collected first and then radiocarbon-dating is applied? If not, what other techniques might have been used?

Scientists recently identified the oldest material on Earth: stardust that's 7 billion years old, tucked away in a massive, rocky meteorite that struck our planet half a century ago.
This ancient interstellar dust, made of presolar grains (dust grains that predate our sun), was belched into the universe by dying stars during the final stages of their lives. Some of that dust eventually hitched a ride to Earth on an asteroid that produced the Murchison meteorite, a massive, 220-lb. (100 kilograms) rock that fell on Sept. 28, 1969, near Murchison, Victoria, in Australia.
New analysis of dozens of presolar grains from the Murchison meteorite revealed a range of ages, from about 4 million years older than our sun — which formed 4.6 billion years ago — up to 3 billion years older than our sun, researchers reported in a new study.


texts: What would be the maximum theoretically possible angular resolution?

texts:
I have studied some basic astronomy, but I have difficulty conceptualizing the physics of luminosity and optics.  We use electromagnetic spectra to detect existence and properties of distant planets, but I am curious about the extent of what could theoretically be optically captured.

(I am unsure if optical is the correct term, but I'm referring to what could be directly captured vs. computed.)

Assuming the use of technology far beyond what we currently are capable of, what is the maximum possible optical angular resolution we could theoretically obtain of a distant sky object?  Or, for example, of the surface topography of an outer planet/moon/dwarf planet?

What would be the limiting factor at the extreme end of possible angular resolution?


texts: Could we parallax measure stars just based on the Earth's size?

texts:
Imagine two major surface observatories, perhaps the "northermost" and "southernmost" such (ideally on a similar longitude).

For nearby stars, could they each take a photo at the same time, and achieve a distance measurement to that star, based on about the size of the Earth as the baseline?

(I appreciate that either of the scopes need only wait a few days, for their viewpoint to have moved a much longer baseline distance!)

Or is that distance far too short?

What then is about the minimum baseline we could parallax-measure the nearest stars, with our currently best telescopes?  100,000km, a million? Far more?


texts: How does the stellar evolution for low and intermediate mass stars differ?

texts:
I'm trying to understand stellar evolutionary tracks for different masses. So far I have the general understanding from a cloud of gas and dust to a white dwarf, neutron star or black hole.
What I don't understand is how the different evolutionary tracks differ from each other for low to intermediate mass stars. I have attached two figures that causes my confusion.
The first one shows many different evolutionary tracks and the second one shows the evolution of a low mass star of 1 Solar mass.
The first image shows that a star of 1 Solar mass stops at point 6, which corresponds to the Helium Core Flash. The second image shows that the evolution continues from this point, making the star bluer before it becomes a red giant again and collapses and explodes.
My question is this: Where does the evolution actually stop? Is the Helium Core Flash the last thing a Sun-like stars experiences or does it in fact follow the rest of the tractory?
All in all, I'm a bit puzzled by the difference between low- and intermediate mass stars evolution. Also it seems to have something to do with conective vs. radiative zones..?
Sorry for the large images!


texts: How are we identifying chemicals in space?

texts:
How do we identify chemicals in space?   For example, how did we find the cloud of methyl alcohol (aka methanol) in W3 (OH) which is 6500 light years away.  I can understand a scope being able to tell something is there, but I don't see how they determine that it is not only alcohol but the type of alcohol.
Here is a link to the W3(OH):  https://phys.org/news/2014-09-alcohol-clouds-space.html
But I am looking for a general answer - as to how we identify chemicals, any chemicals, in space.


texts: How do you find the distance from a star/planet/black hole to another? I know people can calculate the distance from Earth to a star, but what about from one to another?


texts: If blackholes are spherical, what is the prespective of the blackhole image?

texts: If black holes are spherical, so shouldn't it be absorbing light from all the directions? How would one explain the light ring. which seems more like a 2D ring than a sphere?


texts: Can Newton's gravity equation explain why black holes are so strong?

texts: I was just wondering why black hole's gravitational forces are so powerful. I know it's usually explained by Einstein's relativity which states that when an object becomes infinitely dense (a compact mass) it can exert such a force of gravity and warp spacetime. But I also learned about Newton's Law of Gravity equation F = $GM/r^2$. Considering this equation, if the radius of an object becomes super small, then it can technically have immense gravity. So, can the gravitational pull of a black hole be explained by Newton's Law of Gravity or am I missing something? Thanks.


texts: How to calculate the argument of perihelion for exoplanets with incomplete orbital elements?

texts:
I'm trying to simulate the Kepler-444 exoplanetary system using data from this website. The problem is that there is no argument of periapsis parameter for the Kepler-444 system, so while I think I'm getting the correct shape of the orbits, their periapsises and apoapsis are all aligned in the same direction, as you can see in the screen dump below.

So my question is how, or if, I can get the periapsis to be correctly aligned with the data that is available on this website for these planets (unfortunately I can't link to a query, but you can search Kepler-444 and the planets should pop up in the table)? The way I'm doing it now is that I take the semimajor axis and the eccentricity data from the website I linked to, and then I calculate the periapsis for each planet and then I set the x axis to be that value while I let y and z be zero. Once there, I use the vis-viva equation to calculate the velocity vectors for the planet, and then I iterate the simulation forwards in time and get the shapes of the orbits. With the solar system planets, I take the argument of periapsis and the inclination of the orbit and rotate the position and velocity vectors that I derived accordingly, and this way I end up with orbits that have the right shape and their periapsises are correctly aligned, too. Naturally I don't get the right position of a planet in its orbit at a given time using this approach, but for now that is not important; I just want the orbits to have the correct shape and to have their periapsises correctly aligned.

I know very little about orbital mechanics, so any help would be much appreciated so that I can learn something and improve the quality of my simulation.


texts: Comparing Star Formation rate in different galaxies

texts:
I was looking for some scale to compare my result of star formation rate in order to find out whether it is moderate or high or low, but I couldn't find any scale. Is there any paper related to such scale where Star formation rate form minimum to maximum of each galaxy is given and once can compare their result with scale.
I found that one of dwarf galaxies has 0.2 star formation rate, but since I don't have scale to compare, thus I have no clue whether it is high or low or moderate? What is the maximum star formation rate?


texts: Where can I watch the announcement from LIGO about gravitational waves?

texts: Today the LIGO consortium are having a press conference to update us on their search for gravitational waves. How should I watch the announcement?


texts: Is Earth's 1g solid surface gravity unusually high for exoplanets?

texts:
The surface gravities of the Sun’s planets are all close to 1g, 0.38-2.53 (about a factor of e, by chance). The cloud-top gravity of the gas giants is not too interesting here, but I suppose that the gravity on their solid surfaces (if any) does not tend to be higher. So called super-Earth exoplanets seem likely to generally accumulate light gas atmospheres, which decreases their expected solid surface gravity relative to their size as measured during for example transits (I suppose so anyway).

Are there good reasons to expect that in the zoo of planets in the universe, our Earth scores high in the surface gravity top-list? That it is unusual with solid real estate to stand on which has substantially (as in a factor of a few tenths) greater gravity than we have here?

Surface gravities from Wikipedia:

Mercury  0.38
Venus    0.90
Earth    1.00
Mars     0.38
Jupiter  2.53
Saturn   1.07
Uranus   0.89
Neptune  1.14


texts: How would a flat mirror on the Moon reflect sunlight

texts:
I was solving a task that said (paraphrasing):

  There is a flat mirror on the Moon, whose reflection coefficient is 100%, and observers on the Earth observe it as a star whose apparent magnitude is $3^m$. Knowing the magnitude of the Sun is $-27^m$, and its angular diameter is $0.5 {^\circ}$, calculate the diameter of the mirror.

The solution used Pogson's formula to state that the Sun is $1e12$ times brighter than the mirror ... and then the author said it is "obvious" that implies the surface of the mirror's disk in the sky, in $({^\circ})^2$, is $1e-12$ times that of the Sun.

How is it obvious, how do we derive this relation?


texts: What happened to the 2017 proposal on redefining planethood? Is this information available?

texts:
In 2017, Alan Stern et al. submitted a geophysical planet definition to the IAU for review which states
“A planet is a sub-stellar mass body that has never undergone nuclear fusion and that has sufficient self-gravitation to assume a spheroidal shape adequately described by a triaxial ellipsoid regardless of its orbital parameters.”
Obviously, the IAU didn't accept it (as yet) but does anyone know what exactly the IAU stated about the draft and whether it is still being debated or entirely discarded etc.?
I'm just asking if it is possible to know the IAU's reaction. While users may have opinions on how reasonable the proposal is or isn't, please don't post opinions as answers.


texts: What is the theoretical maximum variability a pulsating red giant can have such that a habitable planet can stay habitable for long periods of time?

texts:
I was reading about red giants and came across this statement:

Some research suggests that, during the evolution of a 1 M☉ star along the red-giant branch, it could harbor a habitable zone for several billion years at 2 astronomical units (AU) out to around 100 million years at 9 AU out, giving perhaps enough time for life to develop on a suitable world.

Red giants have luminosities of $\sim 3000 L_\odot$. According to the inverse square law, the habitable zone must be $1^{+1.5}_{-0.2} \cdot \sqrt{3000} \approx 54.772^{+82.158}_{-10.954} \text{AU}$ away from the star. If the star is exhibiting variability, its luminosity may change by about/over $50\%$. This will make the habitable zone vary by a factor of $2\sqrt{0.5}=\sqrt2 \approx 1.414$. So do any stable orbits (in terms of habitability) exist for planets orbiting such a red giant star, assuming the variability timescale is within the orbital period of such a planet?


texts: What are the positions of the Earth, Moon, and Sun at a time when there is the least difference between high and low tides?

texts: Does this happen when there is a full moon?


texts: Solar / lunar positions in ECEF using SOFA C libraries

texts:
I'd like to calculate the positions of the sun and moon in the ECEF coordinate system using the SOFA (http://www.iausofa.org/current_C.html) libraries given a Julian day input.

So far, I've got this process for the sun:  (1) convert Jd (UTC) to TAI, to TT, then to TDB, then (2) calculate earth position/velocity in heliocentric coordinates (iauEpv00), then (3) negate the terms to get ECI.

(a) I'm not sure if the process above is correct, especially since calculating TDB time requires a "dtr" parameter, which apparently you have to have TDB times to estimate using iauDtdb().

(b) I'm not sure how to convert the resulting vector from ECI to ECF, which is probably just a time-based rotation of the longitude, but how much time is elapsing?

(c) Not sure where to even start with the moon.


texts: If Sunlike stars become a red giant and eventually a white dwarf, what do red dwarfs become?

texts: The Sun is said to become a red giant at the end of its life (before that it will become an orange subgiant first and then an orange giant or so) and after ejecting its outer layers it should become a white dwarf. If yellow dwarfs like the Sun become red giants, what do red dwarfs become? Even redder giants? How do the red giants of former red dwarfs (say Proxima Centauri) differ from those of former yellow dwarfs (say the Sun) and how would Proxima's white dwarf be different from the Sun's white dwarf? I mean, a red dwarf's eventual white dwarf would be much less massive than that of the Sun, right?


texts: Convert orbital elements to positions and velocities

texts: I've written a quick and dirty n-body simulator, but currently it requires initial positions and velocities. I've been looking for a way to convert Keplerian orbital elements to positions and velocities. I've searched the web, but I only seem to get conversion from orbital elements to positions and velocities in ECI coordinates, or to a system that orbits the Earth. Ideally, I am hoping that there is an easy conversion between orbital elements and position and velocities for an observer on Earth looking at this n-body system somewhere out in space. I'd appreciate any help in determining this conversion.


texts: Can we use Breakthrough Starshot spacecraft to detect any unknown massive object in our solar system?

texts:
For example, the hypothetical Planet Nine.

Since we just want to prove or rule out the existence of Planet Nine in our solar system, we can avoid most of the technical challenges for StarChip (camera not required, lower propulsion power, etc). So StarChip would become much cheaper, and we are able to launch thousands of the probes, covering a large area of the sky. If a massive object exists within the area, it will affect nearby passing probes and lead to trajectory anomaly, which maybe detectable and the trajectory data can be used for calculating the possible position of the object, and then we can do some follow-up observations and studies using telescopes.

Actually we can use other probes, but StarChip seems cheaper and has faster speed so that we don't have to wait too long if the targets are thousands of AU away from us.

So could this technique be used for detecting Planet Nine or any other unknown massive object in the solar system?
What's the appropriate speed for StarChip so it can accumulate enough gravitational effect to be detectable?


texts: Precision in the measurement of the distance to the Sun

texts:
How precisely can the distance to the Sun be measured? Wikipedia says the distance to the Moon can be measured upto millimeter precision. But Wikipedia article on distance to the Sun says only about Astronomical Unit and nothing on the precision of the measurement of the distance to the Sun. I am certainly aware that we now use radar to measure the distance to the Sun, and I remember reading the precision in its measurement somewhere on the Internet, but I can't find it anymore. When I try to find the relevant information on the Internet, all I find is educational articles on things such as parallax, which is certainly superceded by radar measurements, or articles on lunar distance, which I am not looking for. Relevant references will highly be appreciated.

Edit: I just found out on Internet that we measure the distance to the Sun through distance to the Venus or Mercury. Anyway I want to know the precisions or errors in these measurements..


texts:
I don't have much knowledge of Astronomy but today I was googling randomly and found an article, according to which:

  The moon is of the wrong size for its current orbit.
  The moon rings like a bell when hit by an object, which could signal that it's hollow.
  Metal shavings were found in samples taken by the Apollo crew.
  UFO sightings were common on NASA moon missions.
  All these phenomena and more point toward the suggestion that the moon is actually an artificially created spaceship. It's a bit far fetched, but it's odd that astronomers have been discouraged from testing this theory.

Can this theory be true?


texts: So, what, exactly, is a tropical period?

texts:
From timezone.com's On the Units of Time Part III: The Year February 19, 2001, by Edward Hahn:

Uh, Oh…He’s Going to Ask That Question Again…
So, what, exactly, is a year?

@PM2Ring's comment

FWIW, that's a mean tropical year, which is slightly different to a Vernal Equinox year (~365.242374 days). See https://www.timezone.com/2002/09/25/on-the-units-of-time-part-iii-the-year/

and that includes the following:

(A side note: Some people out there might be wondering why I didn’t use the Tropical Year of 365.24219 days length? In Duncan Steel’s book Marking Time, he points out that both the US Naval Observatory and the Royal Greenwich Observatory make a mistake when saying that, “the tropical year is defined as the mean interval between vernal equinoxes.” This is not astronomically correct – the tropical year is the average time between consecutive occurrences of any date on the calendar. Since the earth on average orbits the sun in the same amount of time regardless of when you start your measurement, shouldn’t they be the same? Well…they aren’t – the vernal equinox year is an average over some number of orbits measured on a single calendar day, while the tropical year averages once more across all the days of the year. The difference is about 16 seconds a year – not much, but even so the people who designed the Gregorian calendar knew enough to aim for the vernal equinox year since they were trying to stabilize the date of Easter, and not the entire year.)

Wikipedia's Tropical year does indeed refer to the Astronomical Almanac Online Glossary (2015) and while the link does not work for me sitting on a bus where I am Wikipedia quotes it:

the period of time for the ecliptic longitude of the Sun to increase 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds.

Question(s):

Is the US Naval Observatory wrong somehow here? Have mistakes been made? Or are there misquotes?
Is it possible to explain in everyday English the geometrical difference between a "Vernal Equinox year" and a tropical year or a mean tropical year?

The basis of an answer may be within the links I've included or it may not be; while "both the US Naval Observatory and the Royal Greenwich Observatory make a mistake" could be true, it's also possible that the blogpost may not have it right, and I can't access the Astronomical Almanac Online Glossary (2015) to resolve the difference.


texts: Is it possible to calculate a star's apparent magnitude in another photometric band knowing its visual magnitude?

texts:
Or, in other words, is it possible to know a star's luminosity in a certain photometric band?
Proxima Centauri's Wikipedia page provides the apparent magntiude in each UBVRIJHK band (getting progressively brighter) as well as the bolometric luminosity and the luminosity in visual wavelengths.
But this amount of information seems limited to Proxima Centauri and a few select other stars.
Is there a way to calculate a star's apparent magnitude/luminosity in another photometric band knowing its visual apparent magnitude/luminosity? Other factors like distance, size, and mass are also known.


texts: How to calculate the integrated source flux density of a continuous source?

texts:
I'm working with data from radio surveys. My images are .fits files with BUNIT Jy/beam. I want to calculate the net flux from a continuous source (not point source). When I simply added all the intensity values and converted it into Jy using the beam parameters, my professor said that it is not enough. He said, "You have to account for noise by taking 3 or 4-sigma level depending on the distribution of the noise". The distribution of noise (at places other than the source) is nearly Gaussian as I can see from a fits viewer.

By "take 3-sigma level", does he mean that I should fit a Gaussian to the noise, find sigma and then choose the pixels with intensity values greater than 3*sigma? If I do this, obviously I lose a lot of pixels. Also, if this is correct, should I subtract the mean of intensity of "noise" pixels from my source intensity?

An RMS noise is given in the header, with a caution that it varies highly around some sources. Is this RMS noise value in anyway related to the sigma that I calculated earlier?


texts:
My question is straight forward.  Is a kilonova bigger than a supernova?

Update

How does a kilonova differ from a nova in terms of...

luminosity
duration
energy
volume of space occupied by the ejecta
speed of the ejecta
other metrics?


texts: Can two heavy objects circling around their C.M. be separated because of the speed of gravity?

texts:
Imagine two massive objects, with the same mass (M) circling around their center of mass (C.M.). Let's assume that the distance between them is 1 light hour. Don´t the two bodies get accelerated and move away from each other because they feel the gravity of each other as it was 1 hour ago, because of which a force tangent to the direction of the speed develops?
Can it be that gravity acts instantaneously? I've read about experiments proving the speed of gravity to be equal to the speed of light, but these were disputed.
Isn't there both in Newtonian mechanics and GR there a time delay? The difference being though that space and time in Newtonian mechanics are separate and absolute (implying instantaneity?), while in GR the both are a whole and absolute.


texts: If I stare at the sun, it's bright and blinding. However, if I look at a star in the sky, it doesn't hurt. What causes this loss of energy that would otherwise damage one's eyes?


texts: Celestron Astromaster 114eq Star pointer finder scope help required

texts:
Just got a Celestron Astromaster 114eq as a christmas present and I have tried setting up the Star Pointer in the daylight. I did not use the red dot method as in the instruction manual, instead, I tried to do this by viewing a object through the main scope (placing the object in the center of the main scope) and then I made some slight adjustments to the Star Pointer finder scope aligning both circle and dots on the finder scope using the two adjustment screws.

This seems to work fine and finds the targets quite well,but when it turns dark and I turn on the the red dot in the finder scope and aim at a star I have yet to manage to focus in on it. Should the method I used to set up the scope finder or do I need to set up the scope finder in the dark?

Any help would be appreciated.


texts:
I am looking for some eyepiece recommendations for my Orion XT8. There are so many kinds out there, and I am not quite sure what to get as recommendations vary wildly. Here are some Q&As that hopefully can give some insight into what I am looking for. Any thoughts or suggestions would be much appreciated.
What kind of telescope do you have?
Orion XT8. Focal length 1200 mm, F/5.9.
I have had it for a little less than a year. Before that I had a 4 inch Orion tabletop reflector.
What kind of eyepieces do you have today?
I have a kit of eyepieces from Canada Telescopes, which seems to be a rebranded imported kit. I can't say much about the quality. It has 6, 9, 15 and 20 mm eyepieces. They have approx 68 deg FOV. The 20 mm is the only semi-usable one, the others aren't really sharp enough.
I also came across a used Celestron Luminos 15 mm. It is nice, but I was underwhelmed by the wider 82 deg FOV. I have heard that these eyepieces do better on other kinds of telescopes that Newtonian reflectors, but I don't know if it is true or not.
What kind of objects do you observe?
Previously it has mostly been the moon and planets. I have spent countless hours looking at Saturn and Jupiter, and recently also Mars that it has been in opposition.
Since a month or so ago, I decided to spend a year trying to observe and check off everything in the book "Turn Left at Orion". That is when the eyepiece problems began :-). The Pleiades requires something wider than I have, and some of the double stars I have been trying to see require higher quality eyepieces for the magnification (dark skies aside).
So, literally a little bit of everything right now.
What magnifications are you looking for?
Low (40x), medium (75x) and high (150x). This means about 30 mm, 16 mm and 8 mm.
Do you wear glasses?
Yes, but I can take them off while observing if that increases my options.
Do you plan to use the eyepieces with another telescope?
Sometime in the future, I'd like to upgrade to a 10 or 12 inch Newtonian. I have been toying with the idea of astrophotography, so perhaps something that would work with a SCT too. But that is much lower priority.
What is your budget?
So hard to answer.
If the recommendation would be for general purpose eyepieces that will help me during my year of visual observation with the XT8 only, then I would like something below 200 USD/eyepiece. Meaning, that if they would be of less value on a 12 inch scope looking at DSOs or a smaller SCT looking at planets, then I'd like to limit the spend.
If the recommendation would be for "forever eyepieces" that are great no matter if it is the XT8, a 12 inch dob or a SCT, then I am more flexible on price because I would know that I could hang on to them for a longer period of time. Perhaps 500 USD/eyepiece maximum (but that would hurt...).
I hope you this gives some valuable context! Thanks!


texts: Candidate major astronomical events circa 600-541 mya?

texts: Are there any known major events around the 50-60 million years preceding the cambrian explosion that could explain the sudden increase in biodiversity?  Specifically a supernova, or active galactic center either in the milky way or some other nearby galaxy?


texts: Could the James Webb Space Telescope detect biosignals on exoplanets?

texts:
The James Webb Space Telescope (JWST) which is slated to launch in 2018 will bring us a better view of exoplanets, but will it be sufficient to detect signs of life on at least some of those worlds?

A good answer will provide an estimate of the James Webb Space Telescope's capabilities to detect atmospheric data relevant to the presence of life.

The preferred answer would also include an analysis of what it would take to say with a decent level of confidence that life was present on an exoplanet and whether or not JWST will be capable of this.


texts: If a black hole has the same mass as me, then why dont i suck everything at my center of mass?

texts: So, a black hole is very dense that you can get really close to its center of mass that it has a strong pull, well, if i have the mass of a black hole that has a really small event horizon, why doesnt my center of mass create an explosion from hawking radiation, or suck myself


texts:
Since the Voyager missions, the atmosphere of Jupiter received great attention, its jet streams made it into text books on geofluid mechanics, including their characteristics like the how they meander, e.g. how likely the formation of throughs and ridges is.
There is a Wikipedia page on Venus' atmosphere mentioning the jet streams:

The upper layer of troposphere exhibits a phenomenon of super-rotation, in which the atmosphere circles the planet in just four Earth days, much faster than the planet's sidereal day of 243 days. The winds supporting super-rotation blow at a speed of 100 m/s (≈360 km/h or 220 mph)4 or more. Winds move at up to 60 times the speed of the planet's rotation, while Earth's fastest winds are only 10% to 20% rotation speed.

This is a good starting point, but I am interested in learning more about the details of Venus' jet streams, like the length scales and dynamics of the jet stream meanders. I have seen images of Venus, but I have troubles already to identify jet streams on many of them, that is why I would appreciate answers with images and/or sketches.
References

W Rossow et. al.: Cloud morphology and motions from Pioneer Venus images, 1981.
Jason Major: Venus’ Winds Are Mysteriously Speeding Up, Universe Today 2013.
Elizabeth Zubritsky: Jet Streams, NASA 2012.


texts:
I am trying to follow this guide and move to a programming language
but I have doubts.

What means the strings A, B and C in this manual?
http://aastro.org/wp-content/uploads/2010/11/Calculation-of-Local-Sidereal-Time.pdf


texts: Does the Sun orbit the Milky way in a (kind of) flat or inclined orbit or more of a sine wave?

texts:
I know it can't be a perfect ellipse or smooth orbit due to all the matter in every direction, and our Sun could be affected by a gravity assist of sorts if it passes close enough to another massive star. I also know that galaxy orbits are different than Solar System orbits because most of the mass is in the dark matter halo and as a result, the outer stars orbit faster than in a standard orbit, so there's a number of variables.

But, if we ignore gravity assists, is the sun mostly in a standard, or lightly inclined orbit around the center of the Milky way or more sinusoidal?

Reason I'm asking - see (attached and in my opinion, bad) article, and picture included.

I've seen pictures like this before that suggests that the Solar System moves in a kind of sine wave motion. I've seen estimates between 26 and 32 million years with the solar-system, rising above then below the plane of the Milky way with consistency (and perhaps, mass extinctions tied to this movement).

I can kind of see that happening, as the sun rises above it might have more gravitational pull below it drawing it back down and you kind of have a horizontal velocity to displacement cycle creating a sine wave in the orbit. That makes logical sense, but I'm wondering if that 26-32 million year sine wave type of movement is generally accepted or more somebody's imagination. Is anything definitive known about stars' orbits within galaxies?


texts: What happens to photons that don't interact with something?

texts:
Say a photon left one of the first stars ever created in our universe.  This photon has been traveling for 13+billion years through the vastness of space without ever hitting anything.  Sure, it's probably been tugged at by gravitational interactions, but it's still happily traveling at the speed of light without direct interaction with matter.

As we know, most of the universe is composed of mostly empty space.  The odds of any single photon hitting something (like the Earth as starlight, etc) would seem to be very small.

What will eventually happen to this photon?  Will it eventually reach the other end of the universe, and if so, what would happen to it there?


texts: How far apart can two people watch the moon simultaneously?

texts:
Obviously there's a limited part of earths surface where the moon is visible at any given time. I imagine the area of this surface would be a lot smaller than the area where the sun is visible at any given time, due to the fact that the moon is a lot closer to earth. But how big is that area exactly?

Or, to put it differently: Imagine you are standing outside your house and looking at the moon. At the exact same moment someone else does the same in another location. But how far apart can you (theoretically) be?


texts: How did we determine the distance of the CMB?

texts: The cosmological microwave background (CMB) is the oldest electromagnetic radiation in the universe. How do we know how far away the CMB is?


texts: Tongue-in-cheek quote on dust extinction

texts:
I remember hearing a quote or maybe rather an anecdote about a famous astronomer but I can't recall the exact wording and I also forgot who allegedly said it. Unfortunately, that has thwarted all my googling attempts.

It goes like this:

The retired astronomer gets asked by a journalist if he would do it all again and he replies something along the lines of:

  Only if selective to total extinction were constant.

Is this something that really happened? If so, who said it and what is the exact wording?

Please also provide a source if possible.


texts: What type of equipment would I need to construct a transit light curve of a planet. It doesn't have to be an exoplanet. If somebody could chuck a list that would be really helpful.


texts:
I have heard that when our solar system formed that all planets except Venus were revolving around the sun in the same direction because of the normal rotation of their axes. Venus was rotating and revolving backwards or retrograde. There was a collision with Venus that caused it to rotate and revolve normally.

But why would a planet revolve backwards around a star relative to all the other planets in the stellar system?


texts: What would happen if we changed Earth's orbit?

texts: If one day we have enough technology to push the Earth away a bit further from the sun to reduce global warming, is it true that it will start to distort the orbits of Mars and Venus, giving them a larger eccentricity and finally colliding with sun or each other?


texts: How is the age of a star on the Henyey track calculated?

texts:
I was reading Stellar Evolution in Early Phases of Gravitational Contraction, by Chushiro Henyey, where he writes,

  If $L \propto R^{-\alpha}$ along the path, the age of a star from the time when $R=\infty$ is given by
  $$t=C/(1-\alpha), C=GM^2/RL=10^{7.20}\left(\frac{M}{M_{\odot}}\right)^2\frac{R_{\odot}}{R}\frac{L_{\odot}}{L}\text{ years}$$
  where $R$ and $L$ are the present values.

This seems to be just for stars on the Hayashi track (and treated here just for Population 1 stars). Is there a similar expression for stars on the Henyey track, or is the same expression valid in both scenarios?


texts: How do we know the radius of the universe is 47 billion light years?

texts: Hubble deep field image at maximum resolution shows a few of the furthest galaxies very small & faint, only just visible, but suggests that there is more to see beyond if only the resolution were high enough. I know the age of the universe is 'only' about 14 billion years, but if Hubble can only show galaxies 13.2 billion light years away, how do we know the radius of the universe is 47 billion light years?


texts: How imperceptible will the 4-July-2020 penumbral lunar eclipse be?

texts:
Wikipedia's July 2020 lunar eclipse; Visibility says:

It will be visible from some parts of North America during moonrise, South and North America, the extreme part of Namaqua Land in South Africa and Western Africa (completely visible), and in southwestern Europe, New Zealand, some parts of The Pacific Ocean, Central, East Africa (except Somalia, Djibouti, Eritrea and a strip of North Eastern Sudan,Egypt and Ethiopia) and some parts of North Africa and some parts of The Indian Ocean during moonset.

But on the sidebar there is an image that shows the outer edge of the penumbra cutting across the center of the Moon at maximum, which means half of the Moon will be full brightness and the other have only partially shadowed by the Earth.
Question: How much darker with the eclipsed half of the Moon get at maximum? Just how "imperceptible" will the 4-July-2020 penumbral lunar eclipse really be?

Source and caption in the main Wikipedia article:

The moon will imperceptibly dim as it passes through the Earth's southern penumbral shadow


texts: Is it possible to use something besides emulsion to directly record the image of a nighttime object using a telescope?

texts:
The following questions have got me thinking.

Is it possible to use Photolithography for telescope image sensor?
Fresnel lenses for a makeshift Galilei telescope?
Has anyone ever tried to make a simple telescope using ice?

A long time ago I think I wrote an answer, or maybe just a series of comments in a different SE site. I think it was Biology SE, and I described ways that people used algae or mold or moss or something in a petrie dish to record a projected image; it photosynthesized faster and grew faster in the brighter areas of the projection.
That's too slow for recording an astronomical image from a telescope.
I don't think the image of the moon from an amateur telescope would be bright enough to burn itself into a small, smooth piece of wood, but I remember something about secret messages written in lemon juice that revealed themselves upon gentle warming.
Is there any way to permanently record a nighttime astronomical image without using a digital imager or photographic emulsion?


texts: Does the Moon Have Enough Water for Robert Zubrin's Mars settlement Plan To Work?

texts: In Robert Zubrin's "The Case for Mars" he outlines a plan to settle Mars by(among other things) finding water and using electrolysis to break up water into Hydrogen and Oxygen. This provides fuel for vehicles and air for the crew to breathe. Can a similar plan work to settle the moon? Are there enough resources on the moon for a settlement to be self-sufficent? Is there enough water on the moon for this to be viable?


texts: Population histograms and relationship between size of galactic disk and amount of dark matter

texts:
I am interested in seeing a plot of dark to baryonic matter ratios in terms of the galactic disk size (when it applies, as not all galaxies fit into disk shapes, and probably analyzing disk galaxies with amorphous ones would only contribute to murky the curve with noise) and how the galactic populations are distributed over that range of sizes.

Does something like this exist?


texts: During solar eclipses on Jupiter, can the moon(s)' shadow(s) on the surface be seen from Earth with a telescope?

texts:
All of the Galilean moons are large and close enough to Jupiter that they can completely eclipse the sun and allow a solar eclipse to happen.

My question is can an observer from Earth, see the moon(s)' shadow(s) on the surface of Jupiter with a telescope or are the shadows too small?


texts: How to compare the observation with the theoretically predicted result?

texts:
On the Wikipedia Article on “Geodesics in general relativity”, it says the following: “Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space.”

Let’s suppose that the planet is, for example, the Mercury far from us. In this case, I think that, for the above “projection onto 3-D space”, it is necessary to extend a Euclidean coordinate system, which is constructed by us living on the Earth, to a region near the Mercury in a simple and continuous manner.

Here, "the extension in the simple and continuous manner" means that three orthogonal basis vectors, defined by an observer on Earth, are used to span the entire universe beyond the earth. That is, in order to compare the observation with the theoretically predicted result, the trajectory of Mercury should be observed and described in terms of coordinates based on the basis vectors.

Similarly, it seems that the extended Euclidean coordinate system is also used in describing galaxies and so forth.  Specifically, if a distance to a star is expressed based on a traveling time of light traveling from the star to us, a distance to a star, which is located beyond the massive black hole at the center of our Milky Way, will be infinity. However, the distance to the star is not expressed in such a manner.  Rather, it seems that the distance to the star is expressed based on the extended Euclidean coordinate system. Is this my understanding correct?

I am a self-taught person who is not good in English. Thus, any comment on technical contents in this article or any improved edition on English expressions would be very welcome.


texts: Should I focus more on Aperture or Focal Length for a telescope?

texts:
Let's assume there are three types of telescopes with the following specifications:

    Telescope                  Aperture              Focal Length
    --------------------------------------------------------------
    Example 1                     70 mm                    400 mm
    Example 2                     60 mm                    700 mm
    Example 3                     60 mm                    900 mm

As a beginner, should I look for a higher value in the aperture or the focal length?


texts: Demo to get Matter Power Spectrum in cosmology

texts:
I would like please to demonstrate the expression of Power spectrum in Cosmology :
First, I have the relative contrast:
$$\delta_{i}(\vec{x}, z) \equiv \rho_{i}(\vec{x}, z) / \bar{\rho}_{i}(z)-1\quad(1)$$
After, we decompose this relative contrast on Fourrier basis :
$$\delta_{i}(\vec{x}, z)=\int \frac{\mathrm{d}^{3} k}{(2 \pi)^{3}} \tilde{\delta}_{i}(\vec{k}, z) \exp (\mathrm{i} \vec{k} \cdot \vec{x})\quad(2)$$
and finally, how to find the following expression (3) from (1) and (2) :
$$\left\langle\tilde{\delta}_{i}(\vec{k}, z) \tilde{\delta}_{i}\left(\vec{k}^{\prime},z\right)\right\rangle=(2 \pi)^{3} \delta_{\mathrm{D}}\left(\vec{k}+\vec{k}^{\prime}\right) P_{i}(\vec{k}, z)\quad(3)$$
?
Any help is welcome.


texts: What are the best candidates for solar lensing of exoplanets, and what would the results be?

texts: If we were able to send a probe to 550AU from the Sun, which exoplanets could be examined, to what resolution, and what form would the examination take?  It is radio telescopy only, or would it be possible to optically see what the surface of an exoplanet looked like?


texts: How precisely is planetary tilt defined (the tilt direction, not just the angle)?

texts: The earth's axis is titled 23.4 degrees with respect to the ecliptic. Since this tilt is responsible for the seasons, it's clear that the tilt is in the direction away from the sun on the shortest day of year in the winter (on the northern hemisphere). That uniquely defines the tilt direction for me. How do we define the tilt direction for the other planets, though? What is the proper way of determining in what direction the tilt of a planet occurs?


texts: Why the space is so dark even there are billions of stars and many quasars emitting light

texts:
In our galaxy itself, there are millions of stars, and there are many more other galaxies in our local group and billions in the observable universes.
For sure they all emit a lot of light, still why the universe is so dark?


texts: When did the Moon become tidally locked to Earth?

texts:
According to various theories the Moon was created around 4.5 billion years ago. About all of these theories suggest that it was rotating around its axis at that time though. Currently, Moon is at tidal lock with Earth, despite some monthly "wiggling" a flat zero on the long-term rotation speed relative to it.

I wanted to ask when did that stop occur - relative to Moon's age, how long was the period of rotating Moon?

The answer would shed some light on my other question - Why are most lunar maria on the visible side? as Earth tends to catch or deflect many bodies heading for Moon surface from "our" direction - still, there is no erosion on the Moon, so craters once formed are extremely slow to vanish - if that period was relatively long, Earth's "protection" wouldn't explain the maria, as rotating Moon would get 'cratered' uniformly all over its surface.


texts: How can I find the depth of a portion of the Valles Marineris?

texts:
How can I find the depth of the low lying part of this image of the western part of Valles Marineris?

I'm interested in the area northeast of Noctis Labyrinthus, southwest of Tithonium Chasma, north of Oudemans, and west of Ius Chasma.

I couldn't find any contour maps of Valles Marineris or Noctis Labyrinthus


texts:
13 billion years ago, the universe was about 600 million years old according to many scientists. At that time, all matter in the universe would have to be closer, or in other words denser.

Did time pass more slowly, at that time, relative to now? I ask, because increased gravity causes time to pass more slowly.

If we'd been there, and measured the speed of light as we measure it today, would the speed of light be different?

Finally, does distant stars look magnified, given that a "tiny" universe is stretched on our entire sky?

I assume then that we'd measure time based on caesium 133 and distance not as a function of the speed of light, but as a theoretical physical "device" that would be the same physical length then and now.


texts: Do we have an accurate breakdown of star types in globular clusters?

texts:
I became interested in the breakdown of star types in globular clusters when trying to give a good answer in a Quora question. I had a difficult time finding an answer.
What I did find out was that what we see is about 10 percent of the stars and they are all as bright or brighter than the sun. Since O, B, A and most F stars are long gone in globulars it appears that most of what we see are red giants. (I know that some blue stars have come to be from stellar collisions in densely packed areas). So if I had to guess, I would say that globulars are 78% main sequence M dwarf, 8 percent MS K dwarf, 2 percent MS G dwarf, 8 percent red giants, 3 percent compact stars (white dwarf, etal.) and 1 percent other.
Also, total mass in literature doesn't seem to agree with star counts in globulars like M3 or M13. Are they including dark matter??


texts: Are there real uses of abstract algebra in astrophysics?

texts:
It is known that a physicist must have, at least in general, a good level in mathematics in order to research and understand other people's works. Linear algebra is a good example, as ODEs and calculus.

I suppose that some astrophysicists have deep knowledge of abstract mathematics and there are some applications of it (for example, I've been told that there is a connection between topology and cosmology). I wondered if there are some field in Astrophysics in which abstract algebra (i.e. fields, rings, category theory...) has been applied.


texts: When was it realised that most major moons orbit in the equatorial plane of their parent planets?

texts: Inspired by the discussion of the moons of Uranus providing a clue to the planet's axis of rotation in this question, I'm wondering when it was realised that the major satellites are typically located in the equatorial plane of their planets. Our own Moon is a counterexample to this trend, so presumably it would have taken a bit of detective work.


texts: What is wrong with my calculations of Jupiter's apparent magnitude?

texts:
I was searching for a formula to calculate the apparent magnitude of a planet knowing its physical characteristics and stumbled upon this answer.
The final formula given is:
$$m_{planet} = V_{planet} + 5 \log_{10}\left( d_{e-p} \right) - 5$$
In which,
$$ V_{planet}=-2.5 \log_{10}\left(a_p \frac{ r_p^2 }{ 4 d_s^2 } \right) - V_{sun}$$
where:

$m_{planet}$ is the planet in question's apparent magnitude,

$V_{planet}$ is the planet's absolute magnitude,

$a_{p}$ is the bond albedo of the planet,

$r_{p}$ is the radius of the planet,

$d_{s}$ is the distance of the planet from its star,

$d_{e-p}$ is the distance between the planet and the observer (here on Earth) in parsecs, and,

$V_{sun}$ is the star's absolute magnitude.

To test it out I tried to calculate the apparent magnitude of Jupiter as seen from Earth at an average opposition. The values then are:

$a_{p} = 0.343$,

$r_{p} = 69,911,000$ m,

$d_{s} = 778.57 \times 10^9$ m (5.204 AU),

$d_{e-p} = 628.97 \times 10^9$ m $= 0.0000203835294968$ parsecs (4.204 AU)

$V_{sun} = 4.83$

All the above values were taken from NASA's Jupiter fact sheet.
Plugging in the numbers and I get $m_{planet} = -10.38$, which is much brighter than the actual apparent magnitude of Jupiter at average opposition of $-2.x$. Where did I go wrong?


texts: Why does Titan have an atmosphere while similar moons such as the Galilean moons don't?

texts: The Galilean moons of Jupiter are similar in size to Titan and are also protected by their parent planet's magnetic field. How come only Titan is able to maintain an atmosphere?


texts: Cancelling out earth rotation speed, Altazimuth mount

texts:
I have a Dobsonian telescope.
It is using Altazimuth mount.
Basic idea of using it is to target the object by moving telescope vertical axis perpendicular to the ground, and an elevation axis that is parallel to the ground.
I have installed two step motors to automate the movement along both vertical and elevation axis.
I would like to find out how can I cancel out earth rotation speed by simultaneously moving both vertical axis and elevation axis motors.
Idea behind it is to point telescope at the object and press the button.
Then the step motors driver software would follow the object as the earth rotate.
I will quote few lines from The Basic Astronomical Telescope Mounting Designs to help me explain what I am trying to achieve:
[Using altazimuth telescope...:]

If you happen to be observing from the North or South Pole, the vertical axis would be aligned with the Earth's spin axis. The nice thing about that would be that when you found an object to observe, rotation in only the vertical axis would be needed to keep the object in the field of view. Rotating at the Earth's spin rate in the opposite direction as the Earth's rotation would keep and object motionless in the eyepiece.
However, for any other latitude on the planet, the vertical axis is not aligned with the Earth's spin axis. This means that to keep an object in the field of view requires motion in both axes. The motion rates will change over time as the elevation angle changes. Tracking objects near the horizon requires mostly changes in elevation, and tracking objects more straight up requires mostly changes in azimuth.

I need to find mathematical algorithm that will help me solve the problem described in the second paragraph.
Hope this is clear.


texts: I've read a few articles written in $2008$ that some stars which have enough mass just collapse into black holes without a supernova, is this proven?


texts:
Does Sun's spectrum expose any red shift at all? Namely, the center of it's visible area (not due to limb effect). If it does, how much is it and does it comply with relativity theory or is it higher/lower than theoretically predicted?

I red about it an article dated 1960 (http://adsabs.harvard.edu/full/1960MNRAS.121..421H) and not sure if new studies show different results. Thanks.


texts: What would happen if those gravitational waves were much stronger?

texts: What if those gravitational waves detected would be actually so strong that the distance of those mirrors moved would be larger? Not 1/1000th of proton but rather one millimeter, or one meter or even more? What would happen to us? How big would these black holes had to be and how much energy would be released in such a process?


texts: Is Limb Darkening because at centre we are directly looking core, whereas at limbs we are seeing only photospheric part?

texts: Is limb darkening of the Sun because at centre we are directly looking the core and different zones, whereas at limbs we are seeing only the photospheric part (and less beneath photospheric part)? Or there is some other physics behind this phenomenon?


texts:
Original question below, but my question is now about how can I supply lat/lon coordinates for other locations other than the one in the example below?

It is possible to use NASA's SPICE toolkit to produce Alt/Az coordinates?  I haven't been able to find any examples.

Update:2
The code below doesn't appear to be along the right lines.  I've posted an answer with the "most" correct code I could come up with.

Update:

I think I partly figured it out.  Apparently most people call it Elevation and Azimuth, not AltAz, which is why I couldn't find anything.  I found a SpiceyPy example which generates the Az, El for DSS-13.  But I'm at a loss as to how to specify the Lat,Lon for general locations.  Looking through the kernel file, the closest thing I see that could be a lat/lon for DSS-13 are the "TOPO_ANGLES" which are -243.2055404763616,-54.7528357325366, which is a pretty odd format if its supposed to be lat,lon.  I was unable to find the real lat/lon for DSS-13, but I was able to find it for DSS-14 which appears in the same file (FYI those coords are 116.89W, 35.426666666666N).  I verified the results with Horizons and they match exactly.

Below I provide a stripped down version of the example to only print out the el/az coordinates.  It requires a file "erotat.tm" which I also provide below.  I was able to filed all of the required kernel files by searching for the name (apparently some of them are quite old).  I was not able to find de414_2000_2020.bsp, but I was able to use de414.bsp from here.  You can install SpiceyPy (assuming you already have Python and PIP) by typing "pip install spiceypy".

import spiceypy

METAKR = 'erotat.tm'
spiceypy.furnsh( METAKR )
et = spiceypy.str2et('2007 JAN 1 00:00:00')
[topov, ltime] = spiceypy.spkpos( 'moon', et, 'DSS-14_TOPO','lt+s', 'DSS-14')
[r, lon, lat] = spiceypy.reclat( topov )

az = -lon
if  az < 0.0:
    az += spiceypy.twopi()
el = lat

print( 'Moon Az (deg):        {0:15.6f}\n'
       'Moon El (deg):        {1:15.6f}\n'.format(
           az * spiceypy.dpr(),
           el * spiceypy.dpr() )  )

spiceypy.unload( METAKR )

Contents of emrotat.tm

KPL/MK

Meta-kernel for the "Earth Rotation" task
in the Binary PCK Hands On Lesson.

The names and contents of the kernels referenced by this
meta-kernel are as follows:

File name                       Contents
------------------------------  ---------------------------------
naif0008.tls                    Generic LSK
de414_2000_2020.bsp             Solar System Ephemeris
earthstns_itrf93_050714.bsp     DSN station Ephemeris
earth_topo_050714.tf            Earth topocentric FK
pck00008.tpc                    NAIF text PCK
earth_000101_070725_070503.bpc  Earth binary PCK

\begindata

KERNELS_TO_LOAD = ( 'naif0008.tls'
                    'de414.bsp'
                    'earthstns_itrf93_050714.bsp'
                    'earth_topo_050714.tf'
                    'pck00008.tpc'
                    'earth_000101_070725_070503.bpc' )

\begintext


texts: I would like to have the discovery papers, notices or announcements done by Herschel with Uranus and Le Verrier with Neptune. I know that Herschel adressed the Royal Society and Le Verrier sent some letters to other european astronomers, but I would like to have the first announcement source if those are available somewhere.


texts: What forces expelled these huge clouds, then blocked further progress, yet allowed it to maintain its threads?

texts:
From Wikipedia and NASA:

Caption: NASA: S74-15583

  (July 1973) --- A huge solar eruption can be seen in this Spectroheliogram obtained during the Skylab 3 mission by the Extreme Ultraviolet Spectrograph/Spectroheliograph SO82A Experiment aboard the Skylab space station in Earth orbit. SO82 is one of the Apollo Telescope Mount experiments. The SO82 A instrument covers the wavelength region from 150-650 angstroms (EUV regions).

The caption may have been written in the 1970's. Is there still a mystery about the forces, or are things somewhat better understood now? The only other (fundamental) force that could be relevant is electric, but I wonder if that was meant to be implicit (as electromagnetic). See statement highlighted in bold below, as the caption continues:

  The magnitude of the eruption can be visualized by comparing it with the small white dot that represents the size of Earth. This photograph reveals for the first time that helium erupting from the sun can stay together to altitudes of up to 500,000 miles. After being ejected from the sun, the gas clouds seem to have come to a standstill, as though blocked by an unseen wall. Some materials appear to have been directed back toward the sun as a rain, distinguished by fine threads. At present it is a challenge to explain this mystery--what forces expelled these huge clouds, then blocked its further progress, yet allowed the cloud to maintain its threads. Both magnetic fields and gravity must play a part, but these curious forms seem to defy explanation based on magnetic and gravitational fields alone. The EUV spectroheliograph was designed and constructed by the U.S. Naval Research Laboratory and the Ball Brothers Research Corporation under the direction of Dr. R. Tousey, the principal investigator for this NASA experiment. On the left may be seen the sun's image in emission from iron atoms which have lost 14 electrons by collision in the sun's million-degree coronal plasma gas.  (emphasis added)

If I understand correctily, this is a telescopic view with a diffraction grating in the optical path - the clear image and its "echoes" are the result of each strong, narrow emission line producing an image at a different angle of the grating's dispersion.


texts: what is the resolution of the magnitude that is distinguishable to the naked eye?

texts:
Or is it possible to spot the changing brightness (magnitude) of a planet with a naked eye

The context of the question is this: If I'm not mistaken Ptolemy was able to say (using observation alone) that the retrograde motion of a planet happen to be when it was closest to earth (that behavior was consistent with his epicycles model).

So I have my doubt with respect to the accuracy that this kind of observation could be done at all.


texts: Why are there no more images revealed by New Horizon?

texts:
Since a few days after the flyby there are no more images published on the NASA page.

Why is NASA waiting to publish any more images for some reason?

Or is there something happened to New Horizon?


texts: If the sun is a second or third generation star, where is the neutron star?

texts: It is widely believed that before the Sun was another star, more pristine in its composition (mostly Hydrogen and perhaps some Helium). And maybe before it was yet another. This blog explains this via the distribution of materials. Now, these previous stars that pre-date the Sun, must have been massive, right? If so, shouldn't they have formed a neutron star or black hole once their lives ended? But there isn't one of those at the center of our solar system. What other stellar evolution paradigm would explain this?


texts: The Three Elements in the Milankovitch Cycles

texts:
According to the Serbian geophysicist Milutin Milankovitch, there are three elements that make an ice age possible:

Eccentricity (orbital shape):  Varying between 0.000055 and 0.0679 over the course of 100,000 years (1.0 being a perfect circle).
Obliquity (axial tilt):  Varying between 22.1 and 24.5 degrees over the course of 41,000 years.
Axial precession (change in the orientation of the rotational axis on a rotating body):  Polaris being the North Star for a total of 26,000 degrees.

The question is how connected those three elements are, in the event someone wants to change the numbers in a worldbuilding process to make either a longer or shorter ice age:

Does the duration and extent of eccentricity affect those of obliquity and precession?

Or does the duration and extent of obliquity affect those of eccentricity and precession?

Or does the duration and extent of precession affect those of eccentricity and obliquity?


texts: Is the flat earth cosmology scientifically justifiable today?

texts: With binoculars or telescopes you'd be able to see to other countries if the earth were flat. And looking out at the ocean we can see where the earth curves and things like the top of ships, not the whole ship. Unless those who think the earth is flat believe they are looking at the end of the world when looking out at the ocean? How do they arrive at this position?


texts:
The Interplanetary Scintillation Array is the radioastronomy observatory (i.e. big antenna) where the first pulsar was discovered by then graduate student Jocelyn Bell Burnell through careful and painstaking review of chart recorder data.

Question: What exactly is interplanetary scintillation; what was the Interplanetary Scintillation Array looking for? Did it successfully observe any?

For observing ionizing radiation such as cosmic rays and photons, a scintillator is used to convert energy to lower energy photons (usually visible light) but I don't know if the term scintillation in radio astronomy is related to that process in any way or not.

update: I've just asked in Aviation SE: What is “scintillation” and are “qualified pilots” aware of it? which was quickly answered and points out that in that context scintillation can also be called "twinkling". If a radio source can twinkle as well, is this an atmospheric effect? If so is it neutrals or ions that generate it. If not, is it turbulence in the ionized interstellar medium?


texts:
"The most massive black holes in the Universe, the supermassive black
holes with millions of times the math [sic] of the Sun will have a
temperature of 1.4 x $10^{-14}$ Kelvin. That's low. Almost absolute zero,
but not quite. A solar mass black hole might have a temperature of
only 0.00000006 Kelvin."
September 5, 2016 by Fraser Cain, Universe Today

Black holes absorb every form of energy, even light. Absorption of energy should raise its temperature but still it is extremely cold, why?


texts: When we are talking about relativistic motions, say from a relativistic jet, what is meant by the term "bulk Lorentz factor", and the bulk speed, $\beta$?


texts: Does the Giant Impact Hypothesis explain how the Moon circularized its orbit?

texts:
I just read most of Wikipedia's article on the Giant Impact Hypothesis. Basically a large object impacts Earth and creates debris that soon coalesces into the Moon.

But there is something I did not find mentioned: How would the Moon get its circular orbit?

A debris field from any impact would at first follow a very elliptical orbit, with a perigee very close to the surface of the Earth and an apogee much farther away. In orbital mechanics, where you start is where you end up. In fact it doesn't even have to be where you start. Pick any point in the orbit and you will return there again. In other words, the original elliptical orbit doesn't change its shape.

...Unless there are pertubations or impacts that change your velocity. How exactly did that happen? Does the GIH just assume something else did that fortuitously?

I've also seen youtube video simulations like this. It's hard to tell if the camera angle is changing or if the orbital plane is unstable (how?), but you can clearly see the debris goes around and impacts the surface again and again. I.e., the orbit remains highly elliptical. I've never seen a simulation that shows the debris circularizing.

I also want to note that this question is highly relavent not just to the Moon, but many other things like orbital capture as well. I've never understood orbital capture theories as they all seem to leave out how the initial elliptical orbit later becomes circular, e.g., Triton.


texts: Could an Earth-like magnetic field protect life at exoplanet Proxima Centauri b?

texts:
I took a look at Wikipedia's page for Proxima Centauri b, the exoplanet that orbits Proxima Centauri, where it is said it is expected to receive 2000 times of stellar wind pressures than on Earth.

It does not say anything about Proxima b having a magnetic field, but I found this paper where a magnetic field for the planet is predicted:

  In our simulations, most Proxima b analogues develop intrinsic dynamos
  that last for 4 Gyr (the estimated age of the host star). If alive,
  the dynamo of Proxima b have a dipole moment . These results are not
  restricted to Proxima b but they also apply to earth-like planets
  having similar observed properties.

My question is if an Earth-like magnetic field, if Proxima b has one, could protect life as it does on Earth, or, conversely, habitability could not be possible due to stellar wind.

Jorge I.Zuluaga, Sebastian Bustamante (2018): "Magnetic properties of Proxima Centauri b analogues". Planetary and Space Science.
Volume 152, March 2018, Pages 55-67


texts:
I've been using binocular for more than a decade for visual observation. I'm thinking of upgrading to a telescope. The Dob caught my attention due to its simplicity in setup and also cost effectiveness. I was thinking of going for 8" or 10" Dob.
What I have also observed is - If I'm going to use dob, I need to keep moving the OTA frequently to keep the focus. If I'm going to use the dob alone, it is not an issue. But my concern is when I want to show the celestial objects to others, I need to frequently move the OTA to keep the objects in focus. It may become tiring if there are many people waiting to watch.
Has anyone encountered similar situation with dob? What are your thoughts? Did you ever feel that you should have gone for go-to mount instead of Dob? Any suggestions please?


texts: What is the upper bound of number of stable interacting stars in a star system?

texts:
I remember very well reading in an article that it's impossible to have a stable star system of 4 or more stars. The article justified its claim discussing about the complexity such systems would have in terms of mass, velocity and distance to be stable. Further more I think there was a constriction related to our 3-dimensional universe, unless I confuse it with an other article about why solar systems cannot form in 4 dimensions... I don't remember though where I read the article.
And since then I thought there couldn't be star system with more than 3 stars and that belief was enforced with the movie Contact when Jody Foster traveled through space and encountered a quadruple star system. What an opportunity for a movie to claim the existence of something so exotic, right?
Recently there's been a fuss about the TIC 168789840 six-tuple system. So either I'm very behind in astronomy news or I confuse the terms Star System and Solar System in the article I read...
Here an article about the aforementioned system.


texts: How bright are the outer planets, when at close range?

texts:
Seven probes have passed by or orbited outer planets. I wonder how their photos differ from the naked eye view one would have if one were actually there.

Saturn is 10 AU from the Sun, which means that it has just 1% of the sunlight we have on Earth. Would an astronaut orbiting Saturn, looking out of the window, even notice that Saturn is there? A clouded winter night on Earth can be really very dark, so you can't see where you put your foot while walking. But the outer planets at least have star light and a wage glimpse of the sun.

Can the light conditions out there be compared to a clear night on Earth with a full moon, half moon or new moon?


texts: Where goes original asteroids mass after impact?

texts: In relation to possible asteroid mining on the moon, where goes asteroid mass after the impact? Will it be burried, scathered, or evaporated?


texts: Can we learn anything from observing galaxies edge-on, like the Spindle Galaxy?

texts:
I was reading about NGC 5866, sometimes referred to as the Spindle Galaxy. It's notable because of its inclination relative to Earth; we see the disk from the side, rather than face-on. The difference is akin to viewing a person's head in profile, instead of looking at their face from the front.

We do lose some information about the morphology of NGC 5866 because of the unusual orientation, as it's difficult to see any spiral arms, bars, or other structures. That said, I'm wondering whether we can still learn more about the galaxy than if we viewed it face-on. For instance, can we gain information about the density distribution of the galaxy at various distances removed from the galactic plane, or perhaps about the structure of its central bulge (if there is one)?


texts: Has the Milky Way collided with another galaxy?

texts: Has the Milky Way ever collided with another galaxy? Or will the collision with Andromeda be our first?


texts: How do satellites impede current telescopes?

texts:
As we send up more and more satellites, it stands to reason that our view of the universe becomes more and more obscured. I would certainly expect for example that a large telescope such as the LSST would be able to see the International Space Station, and since the ISS is not transparent, it wouldn't be able to observe the patch of the sky beyond it.
How do current telescopes currently deal with satellites obstructing their view? Do they simply not observe where the satellite is? If we send up more and more satellites, does it mean that telescopes will have to focus on narrower and narrower fields of view to avoid the swarm?


texts: The earliest life on Earth is thought to have began shortly after its formation (a few hundred million years after, by fossil evidence, and this while the late heavy bombardment was raging). With the next discernible leap (eukaryotes) happening billions of years later, That seems like a very short timeframe for life to spontaneously develop. Is it possible that life was seeded on an early Earth by a supernova of an earlier, life-bearing star, blasting living material across the cosmos?


texts: Orbital resonances and position of planets

texts:
I am interested in quick generation of planetary systems for programs similar to Space Engine or Pioneer Space Simulator. As far as I understand, formation of planets is a complex process and the planet positions are to a great extend given by the orbital resonances, particularly with the gas giant planets. It is very clearly visible in this talk of Sean Raymond.

My question is: How exactly do the orbital resonances affect the stability of the planet trajectories? Which resonances are stable, and which are unstable in the long term evolution of the planetary system?


texts: What is an asteroid called if it is in deep space?

texts:
Pretty much every definition I've read about asteroids is something like "Asteroids are rocky worlds revolving around the sun that are too small to be called planets."

What would an asteroid be called if it was in deep space, not orbiting any sun?


texts: How to adapt small Dobsonian to use with a tripod?

texts:
I am the owner of a small 4", f/6.3 tabletop Dobsonian telescope with a 102mm aperture and 640mm focal length.

It is based on a Dobsonian mount but I would like to use a tripod instead because of the complications of having to cary a table with me everywhere I would like to use the telescope. The alternative is to but the telescope on the ground which makes viewing uncomfortable and is not very stable.

A good tripod could be foldable or collapsible and make my rig much more portable and bring the eyepiece up to a more convenient viewing height, without having to bring along a "telescope table".

Is this possible? If so, are there any specific tripods I should use or other pointers on how best to proceed?

This is not me or my telescope or mount, but it gives an idea of viewing with a similarly-sized tabletop telescope. I'd like to mount the telescope on a tripod instead.

 Source


texts: On orbital mechanics of evaporating planets

texts:
A planet orbits around its sun on an elliptic orbit, and loses mass slowly due to evaporation. How will the parameters of the orbital ellipse change as a function of time?
Could we do a generalisation and mathematically model it?


texts: When is Gamma Draconis closest to the zenith in London on April 4th

texts:
I am reading Roobert Hooke's paper An attempt to prove the motion of the earth from observations (1674, faksimile). Hooke writes

  The principal dayes of doing which will be about the 4 of April, when our Zenith passeth by the said Star at midnight

The said star is Gamma Draconis, and the observations are made in London. As far as I see it, the star is closest to the Zenit at 6 in the morning in London at April 4th.

So, why does Hooke say at midnight? Is this an expression of the 17th century?


texts: Is radiation from neutron stars delayed by time dilation?

texts:
I understand a neutron star to be the densest stuff that can exist without becoming a black hole, the densest thing which directly gives off radiation we can detect. At the event horizon of a black hole, time stands still, in our frame of reference.

Does there exist neutron stars which are very close to getting an event horizon?

Does this "neutron star horizon" cause time dilation, a zone from within of which movement is very slow in our frame of reference?

Could it for example be that the first light from a neutron star itself reaches us billions of years after the light of the supernova of the "classical" star which created the neutron star and its event-horizon like relativistic effects?


texts: How to configure Celestia to work with a spherical mirror projection on a dome

texts:
I find hints around the web, e.g. http://www.cosmodome.net/mirrordome.php that Celestia can be projected on a dome using a spherical mirror projection configuration.

The problem is that I can't find any documentation on how to configure Celestia to warp the generated image, so it can be used in such a projection setup.

For Stellarium\Nightshade I found some references, e.g. from spherical projection guru, Paul Bourke, and I expected to find similar resources for Celestia.

Can Celestia be configured for a spherical mirror projection system?
Can you point me to documentation on how to set up Celestia for a spherical mirror projection system?
Is there a way to warp Celestia with 3rd party tools and then project the images?


texts: Do large telescopes, especially plans for the LSST, avoid saturation artifacts from the brightest stars and planets? If so, how?

texts:
This interesting answer to What is the LSST's plan to address frequent satellite trails in data? quotes:

From the LSST webpage:

The first group of Starlink satellites are sufficiently bright during dawn and dusk (when LSST would be surveying) that the trail would exceed sensor saturation, generating uncorrectable artifacts in the data. If instead these satellites were painted flat black making them a factor of 25 fainter, satellite trails should be less of a challenge for LSST due to its specific design.In that case LSST's frequent imaging of the same region of sky will provide enough data to correct for unsaturated satellite trails or other anomalies.

But now I'm wondering about something a little different. How do large telescopes doing surveys avoid saturation-induced artifacts caused by the brightest stars and planets? Their positions are of course absolutely predictable, so I suppose it's possible to keep their images slightly off of the silicon, and "walk around" them with a series of exposures, is that what the LSST will do?
There are other possibilities, for example a small, mechanical obscuring disk that can be introduced ahead of the CCD to cast a small slightly diffuse shadow, or in the case of multiple CCDs one could put the object between two sensors.
Question: If this is this done in practice, how? Is the LSST planned to have a way to avoid this problem?


texts: Why shouldn't the original singularity of the big bang happen to be the centre of the Universe? Assume that the universe is expanding isotropically with a constant speed.


texts: Can we see the past image of Earth because of curving light by massive objects?

texts: I know massive objects can curve light, can we capture the image of past Earth by lights from Earth that curved by massive objects?


texts:
We have encountered galaxies that act as lenses, magnifying the light coming from behind them. This is super fascinating and it makes me wonder what other optic tools we might have at our disposal.

The question of what we know about our own galaxy is obviously fascinating because it's kind of the the one we have the worst view at. There's so much noise around us it's hard to get a macroscopic view of the galaxy. It occurs to me that if we could stick a mirror out and look at our galaxy from the outside, maybe we have a better view.

Of course, we don't have the technology to make a very useful mirror. And it wouldn't be very efficient. If anything, we would simply launch a probe out there and send back pictures and science data.

But then I got to thinking maybe there's a naturally occurring mirror we could leverage. We know there are entities that can bend light, are there any that bounce it? It would be incredibly advantageous if there was one that allowed us to see our own galaxy, but also it seems unlikely. But are there -any- objects out there that reflect light like a mirror allowing us to see around them or behind them or their "backside"?


texts: How far away would a supernucleus comet be visible?

texts:
If an instrument like LSST quickly spots something as soon as it reaches magnitude 24½, how far away would a 60km first-time visitor from the Oort cloud be when it is spotted? I'm thinking that a huge iceball will make a visible coma sooner, but have no idea what actual numbers would be.

And, given that distance and a parabolic orbit, how much time would that give before it crosses Earth's orbit?


texts: Does the Sun have permanent geographical features?

texts:
Equivalent formulations of this question:

Would it make any sense to draw a map of the Sun?
Is the Sun heterogeneous with respect to latitude and longitude? (I know that it is heterogeneous with respect to altitude/depth)

I know that the Sun does not rotate uniformly, so any map would line up differently as time passes.  However, this does not rule out a slice of the Sun at a given latitude having permanent geographical features, since this slice does rotate uniformly.

Of course, even geographical features on Earth are not really permanent, they change on long time scales.  I don't expect the Sun to have any eternal features, I'm really just thinking about features that change on long time scales, or at least longer than a few months (e.g. not sunspots).


texts: Other side of Earth when the Dinosaur-killer struck

texts:
When the (Chicxulub) asteroid hit Yucatan, what was it like in the minutes, days and weeks afterward on distant locations on Earth?
Related

How loud was the asteroid that killed the dinosaurs?


texts: What is the name of meteoroids which hit Moon, Mars, or pretty much anything that isn’t the Earth?

texts:
A meteorite according to the Oxford English Dictionary is

  A piece of rock or metal that has fallen to the earth's surface from outer space as a meteor.

But, meteors impact other planets.  Are they still meteorites?  Or is there another word for them.  And, if they are still called meteorites, what is the threshold for an object to be impacted upon by a meteor or meteoroid in this case, and still have the meteoroid be called a meteorite.  Are meteoroids impacting Pluto or Pallas meteorites?

We expect the OED to be authoritative so I am just curious if they have let us down or if the clever space brains have a taxonomy to differentiate them.


texts: If interstellar medium was dense plasma and light slowed down, would things appear to move slower far away?

texts: Voyager 2 recently left the solar system and registered an increase in plasma density. If light moved slower in this dense plasma, would it appear like events in other solar systems played out slower than they actually do?


texts: Are there celestial bodies that are about as far away as the Sun?

texts: Just curious. The Sun is 500 light seconds away from the Earth depending on time of the year. The orbit of Mars is about 50% as far as the Sun, the orbit of Vesta about 150%. Is there / Are there celestial bodies inbetween with about the distance of the Sun, their orbit around 93 million miles far from the Earth?


texts: In what parts of the world is it impossible to view the night sky due to light pollution?

texts:
Growing up far from any city, I have always been able to view the full night sky. It was just the way how things were. Of course, I knew that light pollution is a thing, and that the sky is a lot less clear if you live in a city.

It just never occurred to how bad it was before talking with people who had experienced it.

Apparently:

Inside a city, it is pretty much impossible to view anything.
It is not a lot better just outside a city, the sky is still mostly empty.
Most of Europe, parts of the US, India, and eastern Asia is so polluted with light that you can not see the Milky way.

Does anyone have a map showing the affected area? How many people have never seen our own galaxy?


texts:
How can a star's rotation speed be measured?

If stars could be resolved, then you could use the Doppler shift to see that half of the star is bluer and the other half is redder,  but stars (other than our Sun) are seen as point objects. With only one point of measurement, how can the rotation be inferred?

This article mentions that stellar rotation speeds have been measured, but doesn't explain how.


texts:
I would like to calculate how the RA/Dec changes when an object has an apparent linear motionin the equatorial sphere. For example, more or less what an artificial satellite would do in a circular orbit.

In particular, what I'm looking for is as follows:

I have the RA/dec of the object at two times, t1, and t2. Assuming it has a linear motion at constant speed, what RA/dec will it have a t3? So it will have an angular separation proportional to the one it had between t1 and t2, and the three points will form a straight line.


texts:
Would an object shot from earth fall into the sun?

If an object is shot at 107,000 km/h via rocket or otherwise, in the opposite direction to our orbit about the sun, it will be traveling at 0 km/h relative to the sun. The moon is not close enough to the object to have a significant force for the purposes of this question.

Will this object start accelerating towards the sun or will it somehow fall into another stable orbit?

Could it instead get trapped in the L4 Earth-Sun Lagrange point?


texts: Finding equation for energy density of matter

texts:
I'm trying to get an equation for the energy density of matter of the universe $\rho(t)$, assuming the number of particles is conserved and rest mass energy is much greater than kinetic energy. $\rho(t)$ should be a function of the scale factor of the universe $a(t)$, mass of particles $m$, and the number density of the particles $n(t_0)$.

I'm not sure how to approach this since $\rho(t)$ is in units of $\frac{Mass}{Length^3}$, $m$ is in units of $\frac{Mass}{Particle}$, $n(t_0)$ is in units of $\frac{Particle}{Length^3}$, and $a(t)$ is in units of $Length$. I guess there could be a factor of $\frac{a(t)}{a(t_0)}$ or $\frac{a(t_0)}{a(t)}$, but I don't know where I'd get that from.

Any help?

EDIT! I forgot that $a(t)$ is dimensionless.


texts: Meaningful theories of the shape of the universe

texts:
Normally, when people say "the universe is infinite" they generally mean something like "the observable universe is locally flat, it is easy to assume that it is flat way beyond the observable universe, I don't know what lies beyond that, I won't talk about that, that is enough for practical purposes" (or any other proposition implying infinity in any direction and assumed for simplicity's sake while actually focussing on a small region of the space, the observable universe). So, "the universe is infinite" does not seriously mean that physical space goes on forever because this simply makes no sense at all, "infinite" is not a number, it is not a magnitude, it is not a property of real things (if you disagree with this premise please explain how the notion of infinity can be seriously applied to any direction of physical space, i.e. how you can seriously think to extend, sic et simpliciter, such a property of your mathematical model to the real world). (Personally I don't think this should be counted as a theory of the shape of the universe at all).

On the contrary, "the universe is finite and unbounded, compact, closed in all directions" is indeed a meaningful and in principle acceptable theory because it can be thought, described, discussed for what it actually implies. Of course, we don't know what lies beyond the observable universe but the idea of a compact universe makes sense and it seems to me this is the only meaningful explanation currently available of what "could" be (it is not necessarily the right, true explanation, of course).

Is there any other meaningful alternative (which can be thought, described, discussed)? Is there any alternative to the dichotomy "finite universe" vs "infinite universe"? Is there anybody out there working on models that overcome this dichotomy?


texts:
The tidal radius is defined in King (1962) as:

  the value of r (the radius) at which f (the density profile) reaches zero...

This also referred by King as the "limiting radius" written as (Eq 3):

$$r_t=R_{GC}\left(\frac{M}{2M_g}\right)^{1/3}$$

where $R_{GC}$ is the galactocentric distance, $M$ is the cluster's mass, and $M_{g}$ is the galaxy's mass.

This can also be written as Pinfield et al. (1998) Eq (12):

$$r_t = \left( \frac{GM}{2(A-B)^2} \right)^{1/3}$$

where $A$ and $B$ are the Oort constants and $M$ is the total mass.

Now, I've seen the "tidal radius" defined as:

$$r_t=R_{GC}\left(\frac{M}{3M_g}\right)^{1/3}$$

in Chernoff & Weinberg (1990) Eq 2. Notice the 3 in the denominator instead of the 2 as above. According to the authors:

  The tidal radius depends weakly upon the form of the mass distribution of the halo. The Eq. above is correct for the tidal stress of a Keplerian force field. On the other hand, for constant $v_g$, the factor $3M_g$ becomes $2M_g$.

This same quantity (using $3M_g$) is referred to as the "Jacobi radius" in Piatti (2015) Eq 4.

I've also seen the Jacobi radius written as:

$$r_J=\left(\frac{GM}{4\Omega^2-k^2}\right)^{1/3}$$

(where $G, M, \Omega$, and $k$ are the gravitational constant, the cluster
mass, the circular, and the epicyclic frequencies of a near circular
orbit, respectively) in Ernst et al. (2011) Eq (8).

According to Wikipedia, both the tidal and the Jacobi radius are the same thing.

My question: are these two radius the same quantity?